You're going to get quite a few different answers on this one.
For myself, to deal with nibbling and/or biting, my horses will get one hard slap on the mouth within 3 seconds of the offense, as well as me yelling a very firm "NO". Then I will continue on with whatever I was doing as if nothing happened. The key thing is that you have to react immediately within 3 seconds. If 3 seconds pass, don't even bother reprimanding them because they won't correlate it with the wrong behavior.
My horses are not head shy. And my horses do not nibble or bite. They know better.
As far as being pushy, this comes down to how you allow your horse to handle you at all times. If you let them be pushy just once and let me get into your bubble, they are going to think that is okay. So this means whenever you handle your horse, they have got to respect your space.
If I have the halter on and they crowd me, I'm going to stop and back them up away from me. If I'm just with them in the pasture and they come to close, I am going to use my body language to drive them away and out of my bubble. LIke I said, this is something you have to be consistent with and always demand respect and space at all times, with respect being key.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.